Question

The linear momentum $P$ of a particle varies with time as follow $P=a+{bt}^2$. Where $a$ and $b$ are constants. The net force acting on the particle is:

• A. Proportional to $t$
• B. Proportional to $t^2$
• C. Zero
• D. Constant

Answer 1

The correct option is A Proportional to $t$

Given Momentum $P=a+b{t}^2$.

We know force $F=\frac{dp}{dt}=rateofchangeofmomentum$.

$\Rightarrow F=2bt$

or $Force\propto time$.